Global solvability of a boundary value problem for a generalized Boussinesq model is proved in the case, when reaction coefficient depends nonlinearly on concentration of substance. Maximum principle is stated for substance’s concentration. Solvability of control problem is proved, when the role of controls is played by diffusion and mass exchange coefficients from the equations and from the boundary conditions of the model. For a considered multiplicative control problem, optimality systems are obtained. On the base of the analysis of these systems for particular reaction coefficients and cost functionals, local stability estimates are deduced for optimal solutions.

在反应系数非线性地取决于物质浓度的情况下，证明了广义Boussinesq模型边值问题的全局可解性。说明了物质浓度的最大原则。当通过方程和模型边界条件的扩散系数和质量交换系数发挥控制作用时，证明了控制问题的可解性。对于考虑的乘法控制问题，获得了最优系统。在对这些系统的特定反应系数和成本函数进行分析的基础上，推导出局部稳定性估算值以获得最佳解决方案。